Sampling Distributions Stats

Calculate μ_x-bar and σ_x-bar if μ = 794, σ = 48, and n = 64

• μ_x-bar = 794, σ_x-bar = 0.75

• μ_x-bar = 12.4, σ_x-bar = 0.75

• μ_x-bar =794, σ_x-bar = 6

• μ_x-bar = 99.25, σ_x-bar = 6

The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations. Which of the following is the correct ordering of the graphs from least value of n to greatest value of n ?

• A, C, B

• B, A, C

• B, C, A

• C, A, B

• C, B, A

Let x bar be the mean of a random sample of size 50 drawn from a population with mean 112 and standard deviation 40. Find the probability that x bar is between 110 and 114.

• 0.2736

• 0.4286

• 0.0398

• 0.6383

The numerical population of grade point averages at a college has mean 2.61 and standard deviation 0.5. If a random sample of size 100 is taken from the population, what is the probability that the sample mean will be less than 2.51?

• 0.42074

• 0.97725

• 0.02275

• 0.57926

A population has a mean of 12 and standard deviation of 1.5. Find the mean and the standard deviation of the sample mean for samples sizes of 90.

• μx̄=12

  σx̄=1.5

• μx̄=8

  σx̄=1.5

• μx̄=12

  σx̄=0.158

• μx̄=8

  σx̄=0.158

A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values are the true mean and standard deviation for the population of subjects in the study. If a random sample of 144 subjects is selected from the population, what is the approximate probability that the mean of the sample will be more than 11.0 seconds?

• 0.1151

• 0.2743

• 0.7257

• 0.8849

• Based on the values of the true mean and true standard deviation, it can be concluded that the population distribution is not normal and therefore the probability cannot be calculated.

An automobile battery manufacturer claims that its midgrade battery has a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lived of this particular brand is approximately normal. Find the probability that the mean of a random sample of 36 such batteries will be less than 48 months.

• 0.6306

• 0.3694

• 0.0228

• 0.9772

Suppose that in a certain region of the country the mean duration of first marriages that end in divorce is 7.8 years, standard deviation 1.2 years, this is a normal distribution. Find the probability that in a sample of 75 divorces, the mean age of the marriages is at most 8 years.

• 0.4338

• 0.9251

• 0.0749

• 0.5662

When the sample size increases, what happens to the variability of a sampling distribution?

• Increases

• Stays the Same

• Decreases

• We need more indormation

How do you find the sampling distribution of sample means?

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